four design methods & beams Allowable Stress Design Limit State Design Allowable Stress Design

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1 APPLIED ARCHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTES DR. ANNE NICHOLS FALL 013 lecture four Allowable Stress Design historical method a.k.a. working stress, stress design stresses stay in ELASTIC range design methods & beams Forum, Pompeii ethods & Beams 1 Applied Architectural Structures ethods & Beams Allowable Stress Design codes wood National Design Specification anual of Timber Construction (glulam) masonry asonry Specification Joint Code steel Steel Joist Institute American Institute of Steel Construction Limit State Design stresses go to limit (strain outside elastic range) loads may be factored resistance or capacity reduced by a factor based on material behavior state of the art ethods & Beams 3 ethods & Beams 4 1

2 Limit State Design codes wood National Design Specification masonry asonry Specification Joint Code concrete American Concrete Institute Precast & Prestressed Concrete steel American Institute of Steel Construction Reinforced Concrete Design ultimate strength design factor applied to capacity different for flexure, shear, bearing... factors applied to loads (ASCE 7) may be different for combinations U = 1.D + 1.6L U = 1.D + 1.0W + 1.0L can use alternate values & factors (older codes) ethods & Beams 5 ethods & Beams 6 Reinforced Concrete Design want steel to yield first ductile failure underreinforced find flexure capacity or resistance from ultimate stresses in steel uniform stress block in concrete Reinforced Concrete Design ethods & Beams 7 ethods & Beams 8

3 Steel Design load and resistance factor design like concrete, but capacity related to material R u combinations, ex: 1.4D 1.D + 1.6L compression capacity load factors load types R u R n c = 0.85 P n = A g F cr nominal strength resistance factor Plastic Design bending & beams all of material sees ultimate stress refers primarily to steel behavior statically indeterminate systems ethods & Beams 9 ethods & Beams 10 Elastic vs. Plastic Behavior Hooke s law valid f = E yield point is end of elastic range for a ductile material f Internal oments - ALL at yield all parts reach yield plastic hinge forms ultimate moment A tension = A compression continued strain with no more load f y = 50ksi 1 E y = ult or p bc f y 3 y ethods & Beams 11 ethods & Beams 1 3

4 Plastic Hinge Development Plastic Hinge Examples stability can be effected ethods & Beams 13 ethods & Beams 14 Plastic Section odulus shape factor, k = 3/ for a rectangle 1.1 for an I plastic modulus, Z k p k Z Z S f y p y Beams transverse loading sees: bending shear deflection torsion bearing cross section shape ethods & Beams 15 ethods & Beams 16 4

5 Beams maximum stress distribution principal stresses resultant of shear and bending stress Beams deflections d y dx curvature ( x ) EI ethods & Beams 17 ethods & Beams 18 U.Washington ENGR 0 Beams design: bending stress not exceeding allowable or limit stress F all f b c I S req' d F all Beams bending stresses dominate shear stresses exist horizontally with shear no shear stresses with pure bending ethods & Beams 19 ethods & Beams 0 5

6 Beams V & drawings help determine max V + - V ( w )dx Beams prismatic (constant cross section) maximum stress maximum moment non-prismatic S varies + + (V )dx inflection points where slope of =0 L + L ethods & Beams 1 ethods & Beams 1. Know F all for the material or f u for LRFD 4*. Include self weight for max and repeat 3 & 4 if necessary. Draw V &, finding max 3. Calculate S req d 4. Determine section size b h bh S 6 5. Consider lateral stability Unbraced roof trusses were blown down in 1999 at this project in oscow, Idaho. Photo: Ken Carper ethods & Beams 3 ethods & Beams 4 6

7 5. Consider lateral stability (cont) lateral buckling caused by compressive forces at top couples with insufficient rigidity can occur at low stress levels stiffen or brace 6. Evaluate shear stresses - horizontal W and rectangles 3V V max A A web ethods & Beams 5 ethods & Beams 6 6. Evaluate shear stresses (cont) thin walled open or closed ethods & Beams 7 VQ ave Ib VQ q I 7. Provide adequate bearing area at supports P f p A 8. Evaluate torsion T T cross section ethods & Beams 8 + L T τ Tρ J 7

8 8. Torsion (cont) round-ish Tρ τ J J π 1 4 c 8. Torsion (cont) τ max open long sections 1 3 ab T rectangular τ max T c 1 ab ethods & Beams 9 ethods & Beams Evaluate deflections y max & location Deflection Limits based on service condition, severity Use LL only DL+LL Roof beams: Industrial L/180 L/10 Commercial plaster ceiling L/40 L/180 no plaster L/360 L/40 Floor beams: Ordinary Usage L/360 L/40 Roof or floor (damageable elements) L/480 ethods & Beams 31 ethods & Beams 3 8

9 Continuous Beams statically indeterminate reduced moments than simple beam Continuous Beams loading pattern affects moments & deflection max ethods & Beams 33 ethods & Beams 34 Continuous Beams unload end span Continuous Beams unload middle span max max ethods & Beams 35 ethods & Beams 36 9

10 Beam aterials timber glu-lam wood concrete steel reinforced masonry Tools ultiframe in computer lab ethods & Beams 37 ethods & Beams 38 Applied Architectural Structures Tools ultiframe frame window define beam members select points, assign supports select members, assign section load window select point or member, add point or distributed loads Tools ultiframe to run analysis choose Analyze menu Linear plot choose options double click (all) results choose options ethods & Beams 39 ethods & Beams 40 10